How to Add and Subtract
Positive and Negative Numbers

Numbers Can be Positive or Negative:


Negative Numbers (−)	Positive Numbers (+)
(This is the Number Line, read about Using The Number Line)


"−" is the negative sign.	"+" is the positive sign

No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

Example: 5 is really +5

Adding Positive Numbers

Adding positive numbers is just simple addition.

Example: 2 + 3 = 5

is really saying

"Positive 2 plus Positive 3 equals Positive 5"

You could write it as (+2) + (+3) = (+5)

Subtracting Positive Numbers

Subtracting positive numbers is just simple subtraction.

Example: 6 − 3 = 3

is really saying

"Positive 6 minus Positive 3 equals Positive 3"

You could write it as (+6) − (+3) = (+3)

But what happens if we have negative numbers ... ?

Subtracting a Negative is the same as Adding

Example: What is 6 − (−3) ?

6−(−3) = 6 + 3 = 9

Example: What is 14 − (−4) ?

14−(−4) = 14 + 4 = 18

We explain why later!

What About Positive and Negative Together ... ?

You can also have questions like:

What is 6 − (+3) ?
or what is 6 + (−3) ?

They are really the same! Both are subtraction:

Subtracting a Positive
or
Adding a Negative
is
Subtraction

Example: What is 6 − (+3) ?

6−(+3) = 6 − 3 = 3

Example: What is 5 + (−7) ?

5+(−7) = 5 − 7 = −2

And Here Are The Rules

Rule		Example
Two like signs become a positive sign	+(+)	3+(+2) = 3 + 2 = 5
Two like signs become a positive sign	−(−)	6−(−3) = 6 + 3 = 9

Two unlike signs become a negative sign	+(−)	7+(−2) = 7 − 2 = 5
Two unlike signs become a negative sign	−(+)	8−(+2) = 8 − 2 = 6

They are "like signs" when they are like each other (in other words: the same).

So, all you have to remember is:

Two like signs become a positive sign

Two unlike signs become a negative sign

Example: What is 5+(−2) ?

+(−) are unlike signs (they are not the same), so they become a negative sign.

5+(−2) = 5 − 2 = 3

Example: What is 25−(−4) ?

−(−) are like signs, so they become a positive sign.

25−(−4) = 25+4 = 29

Example: What is −6+(+3) ?

+(+) are like signs, so they become a positive sign.

−6+(+3) = −6 + 3 = -3

Start at −6 on the number line, move forward 3, and you end up at −3

Now Play With It!

Try playing Casey Runner, you need to know the rules of positive and negative to succeed!

Why do two negatives make a positive?

Well, first there is the "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive)

But if I say "Do not eat!" I am saying the opposite (negative).

Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).

So, two negatives make a positive, and if that satisfies you, then you don't need to read any more.

Ally's Points

Ally can be naughty or nice. So Ally's parents have said

"If you are nice we will add 3 points (+3).
If you are naughty, we take away 3 points (−3).
When you reach 30 Points you get a toy."

Ally starts the day with 9 Points:

Ally's Mum discovers spilt milk:	9−3 = 6

Then Dad confesses he spilt the milk and writes "undo". Mum calculates:	6−(−3) = 6+3 = 9

So if you subtract a negative, you gain points
(i.e. the same as adding points).

So Subtracting a Negative is the same as Adding

A few days later. Ally has 12 points.

Mum adds 3 points because Ally's room is clean.	12+3 = 15

Dad says "I cleaned that room" and writes "undo" on the chart. Mum calculates:	15 − (+3) = 12

Dad sees Ally brushing the dog. Writes "+3" on the chart. Mum calculates:	12 + (+3) = 15

Ally throws a stone against the window. Dad writes "−3" on the chart. Mum calculates:	15 + (−3) = 12

See: both "15 − (+3)" and "15 + (−3)" result in 12.

So:

It doesn't matter if you subtract positive points
or add negative points,
you still end up losing points.

So, Subtracting a Positive
or
Adding a Negative
is
Subtraction

Try These Exercises ...

Now try This Worksheet, and see how you go.

And also try these questions:

How to Add and Subtract Positive and Negative Numbers